Calculation Final Values, Test4
Paloma Contreras
2025-06-09
Last updated: 2025-06-09
Checks: 7 0
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HairCort-Evaluation-Nist2020/
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Summary
Cortisol value calculations (includes bad quality samples, n = 41)
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | NA’s | |
|---|---|---|---|---|---|---|---|
| A) Standard Method (mult. by sample dilution) | 17.13 | 29.01 | 32.27 | 35.28 | 39.47 | 82.94 | 4 |
| B) Spike-Corrected Method (Nist 2020) | -35.83 | 10.61 | 17.00 | 19.97 | 30.62 | 123.07 | 4 |
| C) Spike-Corrected (Sam’s Method) | 11.8 | 19.45 | 29.34 | 29.54 | 33.1 | 82.90 | 4 |
Cortisol value calculations (removed bad quality samples)
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | |
|---|---|---|---|---|---|---|
| A) Standard Method (mult. by sample dilution) | 18.27 | 29.27 | 31.54 | 34.13 | 37.73 | 69.17 |
| B) Spike-Corrected Method (Nist 2020) | -39.371 | -34.855 | -20.577 | -14.325 | -6.825 | 40.400 |
| C) Spike-Corrected (Sam’s Method) | ** 11.80** | 22.14 | 28.91 | 27.13 | 31.88 | 40.40 |
Plate description
| Category | Description |
|---|---|
| TA | Non-spiked serial dilution |
| TB | Spiked only in first dilution (TB1) then serially diluted |
| TC | Each dilution individually spiked with 25 µL of std1 |
| TD | First tube spiked 1:1 with std1 (110 µL), then serially diluted |
| TP | Precision replicates (different weights: 6, 9, 12 mg) spiked with 25 µL |
Results:
Intra-assay CV: 14.48%
Intra-assay CV after removing low quality samples: 4.76%
Inter-assay CV: 21% (Bindings for 20mg sample diluted in 250 uL, no spike: 64.8% and 48% in test3 and test4, respectively)
Conclusions:
Concerns: Overall quality of the plate is not great, but serial dilusions show clear parallelism and standards have values within the expected
Explanation of each variable used in calculations
Ave_Conc_pg/ml: average ELISA reading per sample in pg/mL
Weight_mg: hair weight in mg
Buffer_nl: assay buffer volume in nL → we convert to mL
Spike: binary indicator (1 = spiked sample)
SpikeVol_uL: volume of spike added in µL
Dilution: dilution factor (already present)
Vol_in_well.tube_uL: total volume in well/tube in µL (for spike correction)
std: standard reading value
extraction: methanol volume ratio = vol added / vol recovered (e.g. 1/0.75 ml)
Cortisol concentration calculations
Parameters and unit transformations:
# Volume of methanol used for cortisol extraction varies, so it is included in file
# as Extraction_ratio (vol added / vol recovered) in mL
# Reading of spike standard and conversion to ug/dl
std <- 3209.5 # test 4 backfit
std_ul.dl <- std / 10000 # std in ul/dl
# Creating variables in indicated units
df$Buffer_ml <- c(df$Buffer_nl/1000) # dilution (buffer)
df$Ave_Conc_ug.dl <- c(df$Ave_Conc_pg.ml/10000) # Transform to μg/dl from assay outputIdentify and flag bad quality samples
ABOVE 80% binding HIGH CV HIGH CV;ABOVE 80% binding
4 2 7
HIGH CV;UNDER 20% binding OK UNDER 20% binding
1 60 8 Summary CV for all samples: Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.00 2.70 5.90 14.48 14.10 87.50 41 Summary CV for good quality samples only: Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.000 2.570 3.600 4.762 7.100 14.100 41 (A) Standard Calculation
Formula:
((A/B) * (C/D) * E * 10,000) = F
- A = μg/dl from assay output;
- B = weight (in mg) of hair subjected to extraction;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract;
- F = final value of hair CORT Concentration in pg/mg
##################################
##### Calculate final values #####
##################################
data$Final_pg.mg_A <- c(
((data$Ave_Conc_ug.dl / data$Weight_mg) * # A/B *
data$Extraction_ratio * # C/D *
data$Buffer_ml * 10000)) # E * 10000 Summary of all samples (n = 37 ): Min. 1st Qu. Median Mean 3rd Qu. Max.
17.13 29.02 32.27 35.28 39.47 82.93 Summary for good quality samples only (n = 18 ): Min. 1st Qu. Median Mean 3rd Qu. Max.
18.27 29.27 31.54 34.13 37.73 69.17 (B) Accounting for Spike
We followed the procedure described in Nist et al. 2020:
“Thus, after pipetting 25μL of standards and samples into the appropriate wells of the 96-well assay plate, we added 25μL of the 0.333ug/dL standard to all samples, resulting in a 1:2 dilution of samples. The remainder of the manufacturer’s protocol was unchanged. We analyzed the assay plate in a Powerwave plate reader (BioTek, Winooski, VT) at 450nm and subtracted background values from all assay wells. In the calculations, we subtracted the 0.333ug/dL standard reading from the sample readings. Samples that resulted in a negative number were considered nondetectable. We converted cortisol levels from ug/dL, as measured by the assay, to pg/mg—based on the mass of hair collected and analyzed using the following formula:
A/B * C/D * E * 10,000 * 2 = F
where
- A = μg/dl from assay output;
- B = weight (in mg) of collected hair;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract; 10,000 accounts for changes in metrics; 2 accounts for the dilution factor after addition of the spike; and
- F = final value of hair cortisol concentration in pg/mg”
- SPd = sample dilution factor (if serially diluted)
##################################
##### Calculate final values #####
##################################
# spike is already divided by 10000 (unit is ug/dL)
data$Final_pg.mg_B <-
ifelse(
data$Spike == 1, ## Only spiked samples
((data$Ave_Conc_ug.dl - (std_ul.dl)) / # (A-spike)
data$Weight_mg) # / B
* data$Extraction_ratio * # C / D
data$Buffer_ml * 10000 * 2, # E * 10000 * 2
data$Final_pg.mg_A
)Summary all samples: Min. 1st Qu. Median Mean 3rd Qu. Max.
-35.83 10.61 17.00 19.97 30.62 123.07 Summary good quality samples only: Min. 1st Qu. Median Mean 3rd Qu. Max.
-35.83333 0.08417 14.03600 10.92278 23.88333 40.39865 (C) Sam’s calculation
Simplifies unnecessary unit transformations and accounts for spike considering dilution of both sample and the spike
- Step 1: Calculate contribution of the spike
- Step 2: Substract spike from plate reading values and calculate final values accounting for dilution of the sample, weight, and reconstitution
Step 1: Calculate contribution of spike
X * Y / Z / SPd = SP
- SP = final value of spike contribution in pg/mL
- X = volume of spike added (mL)
- Y = concentration of the spike added (pg/mL)
- SPd = if serially diluted, dilution factor for the spike (i.e: 1, 2, 4, 8, etc.)
- Z = total volume (mL) in the well or tube, if spike is added before loading the plate (sample + spike)
# Transforming units
data$SpikeVol_ml <- data$SpikeVol_ul/1000 # X to mL
data$Vol_in_well.tube_ml <- data$Vol_in_well.tube_ul/1000 # Z to mL
# Calculate spike contribution to each sample
## ( Spike vol. x Spike Conc.)
## ------------------------ / dilution = Spike contribution (pg/ml)
## Total vol.
# Calculate cort contribution of spike to each sample
data$Spike_contribution <- ((data$SpikeVol_ml * std / # X * Y
data$Vol_in_well.tube_ml) / # Z /
data$Dilution_spike) # SPThe reading for standard 1 in this plate is 3209.5The total contribution of the Spike to each sample is can be any of the following numbers (in pg/ml) [1] 0.000000 291.772727 160.475000 80.237500 40.118750 20.059375
[7] 10.029688 5.014844 1604.750000 802.375000 401.187500 200.593750
[13] 100.296875 50.148438 25.074219 1604.750000Step 2 : Substract spike and calculate final values
((A - SP)/B) * (C/D) * E = F
- A = pg/ml from assay output;
- SP = spike contribution (in pg/ml)
- B = weight (in mg) of hair subjected to extraction;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract;
- F = final value of hair CORT Concentration in pg/mg.
##################################
##### Calculate final values #####
##################################
data$Final_pg.mg_C <-
(((data$Ave_Conc_pg.ml - data$Spike_contribution)) / # (A - spike)
data$Weight_mg) * # / B *
data$Extraction_ratio * # C / D *
data$Buffer_ml # E Summary for all samples: Min. 1st Qu. Median Mean 3rd Qu. Max.
11.80 19.45 29.34 29.54 33.10 82.90 Summary for good quality samples only: Min. 1st Qu. Median Mean 3rd Qu. Max.
11.80 22.14 28.91 27.13 31.88 40.40 | Sample | Final_pg.mg_A | Final_pg.mg_B | Final_pg.mg_C | Spike_contribution | Binding.Perc | SpikeVol_ul | Dilution_sample | Dilution_spike | Extraction_ratio | |
|---|---|---|---|---|---|---|---|---|---|---|
| 32 | TP2A | 33.71556 | 10.373333 | 19.45111 | 1604.75 | 17.3 | 25 | 1 | 1 | 1.333333 |
| 33 | TP2B | 27.56444 | -1.928889 | 13.30000 | 1604.75 | 21.1 | 25 | 1 | 1 | 1.333333 |
| 34 | TP2C | 32.30222 | 7.546667 | 18.03778 | 1604.75 | 18.1 | 25 | 1 | 1 | 1.333333 |
| 35 | TP3A | 69.17117 | -20.686937 | 29.41385 | 1604.75 | 23.2 | 25 | 1 | 1 | 1.351351 |
| 36 | TP3B | 28.06667 | 13.340000 | 17.36833 | 1604.75 | 15.5 | 25 | 1 | 1 | 1.333333 |
| 37 | TP3C | 31.07333 | 19.353333 | 20.37500 | 1604.75 | 13.9 | 25 | 1 | 1 | 1.333333 |
Plots: all samples vs final concentration
(A) Standard Calculation
Final cortisol concentrations not accounting for spike. Tags are sample numbers.
Expected results: a straight horizontal line showing that I obtained same cortisol concentration value in the Y axis, across different sample weights.
(B) Accounting for Spike
Final cortisol concentrations accounting for Spike as instructed in Nist et al. 2020.
Expected results: lower values than in the previous plot for the spiked samples, but not as low as negative samples (for all of them). Spiked and non-spiked samples should be aligned (same concentration across different weights)
(C) Sam’s calculation
Final cortisol concentration values using new method.
Expected results: one unique horizontal line, regardless of the spiking status and dilution.
| Version | Author | Date |
|---|---|---|
| dd200fc | Paloma | 2025-04-23 |
Plot contribution of spike vs sample quality (C)
Plot grouped by reconstitution volume
Plot grouped by category (C)
`geom_smooth()` using formula = 'y ~ x'
| Version | Author | Date |
|---|---|---|
| b7150cb | Paloma | 2025-04-29 |
Error evaluations, grouped by data quality (using C)
Number of good quality datapoints: 18Models used with respect to weight:
lm(Final.pg.mg_C ~ Weight_mg,
data = data2.hq)Error using good quality samples only
Mean Absolute Error (MAE) ALL: 4.774 Standard Deviation of Residuals ALL: 6.21 Error using all samples
Mean Absolute Error (MAE) ALL: 7.633 Standard Deviation of Residuals ALL: 11.358
sessionInfo()R version 4.5.0 (2025-04-11)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.5
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/Detroit
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] dplyr_1.1.4 paletteer_1.6.0 broom_1.0.8 ggplot2_3.5.2
[5] knitr_1.50
loaded via a namespace (and not attached):
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[5] lattice_0.22-6 stringi_1.8.7 digest_0.6.37 magrittr_2.0.3
[9] evaluate_1.0.3 grid_4.5.0 fastmap_1.2.0 Matrix_1.7-3
[13] rprojroot_2.0.4 workflowr_1.7.1 jsonlite_2.0.0 whisker_0.4.1
[17] backports_1.5.0 rematch2_2.1.2 promises_1.3.2 mgcv_1.9-1
[21] purrr_1.0.4 scales_1.3.0 jquerylib_0.1.4 cli_3.6.4
[25] rlang_1.1.6 splines_4.5.0 munsell_0.5.1 withr_3.0.2
[29] cachem_1.1.0 yaml_2.3.10 tools_4.5.0 colorspace_2.1-1
[33] httpuv_1.6.16 vctrs_0.6.5 R6_2.6.1 lifecycle_1.0.4
[37] git2r_0.36.2 stringr_1.5.1 fs_1.6.6 pkgconfig_2.0.3
[41] pillar_1.10.2 bslib_0.9.0 later_1.4.2 gtable_0.3.6
[45] glue_1.8.0 Rcpp_1.0.14 xfun_0.52 tibble_3.2.1
[49] tidyselect_1.2.1 rstudioapi_0.17.1 farver_2.1.2 nlme_3.1-168
[53] htmltools_0.5.8.1 rmarkdown_2.29 labeling_0.4.3 compiler_4.5.0